#ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP

#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <boost/random/exponential_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
#include <limits>

namespace stan {
  namespace math {

    template <typename T_y, typename T_scale, typename T_shape>
    typename return_type<T_y, T_scale, T_shape>::type
    pareto_cdf(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
      typedef typename stan::partials_return_type<T_y, T_scale, T_shape>::type
        T_partials_return;

      if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
        return 1.0;

      static const char* function("pareto_cdf");

      using std::log;
      using std::exp;

      T_partials_return P(1.0);

      check_not_nan(function, "Random variable", y);
      check_nonnegative(function, "Random variable", y);
      check_positive_finite(function, "Scale parameter", y_min);
      check_positive_finite(function, "Shape parameter", alpha);
      check_consistent_sizes(function,
                             "Random variable", y,
                             "Scale parameter", y_min,
                             "Shape parameter", alpha);

      VectorView<const T_y> y_vec(y);
      VectorView<const T_scale> y_min_vec(y_min);
      VectorView<const T_shape> alpha_vec(alpha);
      size_t N = max_size(y, y_min, alpha);

      OperandsAndPartials<T_y, T_scale, T_shape>
        operands_and_partials(y, y_min, alpha);

      // Explicit return for extreme values
      // The gradients are technically ill-defined, but treated as zero
      for (size_t i = 0; i < stan::length(y); i++) {
        if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
          return operands_and_partials.value(0.0);
      }


      for (size_t n = 0; n < N; n++) {
        // Explicit results for extreme values
        // The gradients are technically ill-defined, but treated as zero
        if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
          continue;
        }

        const T_partials_return log_dbl = log(value_of(y_min_vec[n])
                                              / value_of(y_vec[n]));
        const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
        const T_partials_return alpha_dbl = value_of(alpha_vec[n]);

        const T_partials_return Pn = 1.0 - exp(alpha_dbl * log_dbl);

        P *= Pn;

        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n]
            += alpha_dbl * y_min_inv_dbl * exp((alpha_dbl + 1) * log_dbl)
            / Pn;
        if (!is_constant_struct<T_scale>::value)
          operands_and_partials.d_x2[n]
            += - alpha_dbl * y_min_inv_dbl * exp(alpha_dbl * log_dbl) / Pn;
        if (!is_constant_struct<T_shape>::value)
          operands_and_partials.d_x3[n]
            += - exp(alpha_dbl * log_dbl) * log_dbl / Pn;
      }

      if (!is_constant_struct<T_y>::value) {
        for (size_t n = 0; n < stan::length(y); ++n)
          operands_and_partials.d_x1[n] *= P;
      }
      if (!is_constant_struct<T_scale>::value) {
        for (size_t n = 0; n < stan::length(y_min); ++n)
          operands_and_partials.d_x2[n] *= P;
      }
      if (!is_constant_struct<T_shape>::value) {
        for (size_t n = 0; n < stan::length(alpha); ++n)
          operands_and_partials.d_x3[n] *= P;
      }
      return operands_and_partials.value(P);
    }

  }
}
#endif
